• Weinan E.A Proposal on Machine Learning via Dynamical Systems link

  The first one uses the forward dynamic to describe the residual network.

• Bo Chang, Lili Meng, Eldad Haber, Lars Ruthotto, David Begert, Elliot Holtham. Reversible Architectures for Arbitrarily Deep Residual Neural Networks arXiv

  Using Hamilton ODE to approach linearize stable. Approach better result when the number of label data is small.

• Sho Sonoda, Noboru Murata. Double Continuum Limit of Deep Neural Networks arXiv
• Zhen Li, Zuoqiang Shi. Deep Residual Learning and PDEs on Manifold arXiv

  The ODE which is the continuum limit of the residual net is the characteristics of a transport equation.

• Yiping Lu, Aoxiao Zhong, Quanzheng Li, Bin Dong. Beyond Finite Layer Neural Network: Bridging Deep Architects and Numerical Differential Equations
• Bo Chang, Lili Meng, Eldad Haber, Lars Ruthotto, David Begert, Elliot Holtham. MULTI-LEVEL RESIDUAL NETWORKS FROM DYNAMICAL SYSTEMS VIEW
• Qianxiao Li, Long Chen, Cheng Tai, E Weinan Maximum Principle Based Algorithms for Deep Learning arXiv

Ref: http://about.2prime.cn/pde.html (微信群中陆一平-北京大学-数学)